Problem 16 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

\(\mathrm{Na}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]\) is diamagnetic, not paramagnetic. Use this information to determine the geometry of the anion. (Section \(28.7)\)

Step-by-Step Solution

Answer

The geometry of the anion \([\text{Ni}(\text{CN})_4]^{2-}\) is square planar.

Step 1: Understanding the Problem

We are given that the compound \(\text{Na}_2[\text{Ni}(\text{CN})_4]\) is diamagnetic. Diamagnetism occurs when all electrons are paired in an atom or molecule, leading to no net magnetic moment.

Step 2: Determine the Electronic Configuration of Ni

The central metal atom Ni (Nickel) in the anion has an atomic number of 28. In its ground state, Ni has an electronic configuration of \([\text{Ar}] 3d^8 4s^2\).

Step 3: Removing Electrons for Nickel in the Complex

Nickel in the complex is in a +2 oxidation state, as each sodium atom contributes +1 to balance the -4 charge of \([\text{Ni}(\text{CN})_4]^{2-}\). Thus, we remove two electrons from the 4s orbital: \([\text{Ar}] 3d^8\).

Step 4: Ligand NC^- Influence and Orbital Hybridization

CN^- (cyanide) is a strong field ligand and causes pairing of the electrons in the \(3d\) orbitals. In a low-spin or strong field case like this one, the internal pairing leads to a \(d^8\) orbital configuration that uses hybrid \(dsp^2\) orbitals.

Step 5: Determining the Geometry

The \(dsp^2\) hybridization implies that orbitals reshape themselves into a square planar geometry. This configuration is consistent with the nickel complex being diamagnetic, as all electrons remain paired.

Key Concepts

Diamagnetism

Diamagnetism is a fascinating property of materials that arises when all the electrons in an atom or molecule are paired. This means there are no unpaired electrons to contribute to a magnetic field, resulting in the material being repelled by magnets. In the context of coordination compounds, identifying whether a compound is diamagnetic or paramagnetic can offer clues about the electron configuration and the geometry of the molecule.

• Diamagnetism is weak compared to paramagnetism but is a definitive sign of electron pairing.
• It is contextually important; if a compound is known to be diamagnetic, it indicates that the electrons have been influenced to pair up, often due to the nature of the ligands involved.
• Materials like bismuth and copper are classic examples of diamagnetism, being slightly repelled by magnets.

This property is crucial when predicting the behavior or even the geometry of complexes in coordination chemistry. Often, the type of ligands, such as CN⁻ in our example, strongly affects electron pairing and can lead to a diamagnetic state.

Square Planar Geometry

Square planar geometry is a common geometry observed in certain coordination compounds, typically with metal centers having a d⁸ electronic configuration in a strong ligand field like that caused by CN⁻. In such a geometry, the metal atom is centrally located, surrounded symetrically by four ligand atoms, all situated in the same plane.

• It offers a distinctive flattened square shape to the molecule, quite different from other geometries like tetrahedral.
• This structure is facilitated by the dsp² hybridization, indicating a lower energy state due to pairing of electrons.
• Square planar complexes are often associated with transition metals such as nickel, palladium, and platinum, usually in the +2 oxidation state.

The preference for this geometry can be strongly influenced by ligand strength and electron configuration. The planar nature makes the molecular geometry distinct from the more common tetrahedral form seen without such strong field ligands.

Electron Configuration

Electron configuration is vital in understanding the behavior and properties of atoms and their complexes. It describes how electrons are distributed among the atomic or molecular orbitals. Specifically, in the case of \[\mathrm{Ni}^{2+}\], we derive the configuration by considering its core electrons and the effects of the ligand field.

• Nickel in its Ground State: \[\mathrm{[Ar]} \, 3d^8 \, 4s^2\]
• Ni after Losing 2 Electrons (Ni²⁺): \[\mathrm{[Ar]} \, 3d^8\]

In coordination chemistry, especially with strong field ligands like cyanide (CN⁻), it's crucial to consider electron pairings within d orbitals. Strong field ligands impose a significant effect, splitting the d orbitals to encourage electron pairing, as seen in Ni’s case.
This reconfiguration results in a low-spin state, often essential for understanding the resulting geometry and magnetic properties of the complex.

Hybridization

Hybridization is a concept used to describe the mixing of atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds. In coordination compounds, hybridization helps explain the electron sharing between the central metal and its ligands and is crucial in determining the molecular geometry.

• For Nickel in the Diamagnetic Complex: \[dsp^2\] Hybridization leads to a square planar configuration.
• This results from the involvement of one d orbital, one s orbital, and two p orbitals merging to form four hybrid orbitals.
• These hybridized orbitals are symmetric, allowing CN⁻ ligands to attach in the square planar arrangement.

Hybridization is particularly important because it affects not only geometry but also the ligands' ability to influence magnetic properties by dictating electron arrangement.
This hybridization fundamentally determines why diamagnetism occurs, as it encourages paired electron formations due to the high ligand field strength.